Abstract In the present investigation the geometrically nonlinear post buckling analysis of laminated composite doubly curved shells is presented using finite element method. The finite element model includes the general geometric nonlinearity due to large deflection. The present nonlinear strain displacement relations are expressed in the curvilinear coordinates. The material behaviour is, however, assumed to be linear and elastic. The principle of virtual work forms the basis to derive the nonlinear finite element equations. To solve the nonlinear finite element equations an incremental iterative technique based on the arc length method is employed. The present results are found to compare well with those available in the literature and are also able to capture both snap through and snap back post buckling behaviour. The nonlinear responses of three specially laminated spherical, cylindrical and conoidal shells are analyzed and the results are discussed.